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Material and Capacity Requirements Planning withdynamic lead times.
Herbert Jodlbauer, Sonja Reitner
To cite this version:Herbert Jodlbauer, Sonja Reitner. Material and Capacity Requirements Planning with dy-namic lead times.. International Journal of Production Research, Taylor & Francis, 2011, pp.1.�10.1080/00207543.2011.603707�. �hal-00724885�
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Material and Capacity Requirements Planning with dynamic
lead times.
Journal: International Journal of Production Research
Manuscript ID: TPRS-2010-IJPR-0906.R2
Manuscript Type: Original Manuscript
Date Submitted by the Author:
24-May-2011
Complete List of Authors: Jodlbauer, Herbert; FH-Studiengange Steyr, Operations Management Reitner, Sonja; FH-Studiengaenge Steyr, Operations Management
Keywords: MRP, CAPACITY PLANNING
Keywords (user): Material requirements planning, Dynamic lead times
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Material and Capacity Requirements Planning with dynamic lead
times
Herbert Jodlbauer*, Sonja Reitner
Department of Operations Management, Upper Austrian University of Applied
Sciences, Steyr, Austria
Wehrgrabengasse 1-3, 4400 Steyr, Austria, Tel.: +43 (0)7252 884-3810, Fax.: -3199
(Received XX Month Year; final version received XX Month Year)
Traditional MRP does not consider the finite capacity of machines and assumes fixed
lead times. This paper develops an approach (MCRP) to integrating capacity planning
into material requirements planning. To get a capacity feasible production plan different
measures for capacity adjustment such as alternative routeings, safety stock, lot splitting
and lot summarization are discussed. Additionally, lead times are no longer assumed to
be fixed. They are calculated dynamically with respect to machine capacity utilisation. A
detailed example is presented to illustrate how the MCRP approach works successfully.
Keywords: MRP, Material Requirements Planning, capacity planning, dynamic lead times
1. Introduction
Conventional enterprise resource planning (ERP) material planning methods are
based on material requirements planning (MRP), a production planning system
developed by Orlicky (1975). The MRP steps for each level in the bill of material
(BOM), beginning with the end items, are netting, lot sizing, offsetting and the BOM
explosion (see Figure 1). Two of the most important weak points of MRP are the
assumptions of infinite machine capacity and of production lead times which are
constant or depend on lot size, processing and setup time. In practice, lead times
depend on many factors such as machine utilization, lot size, inventory and
dispatching rules and are thus variable. Kanet (1986) shows that using fixed lead
times results in over-planning of inventory at every level.
Ignoring finite machine capacity leads to capacity infeasible schedules which
have to be revised by the user. Although the capacity requirements planning (CRP)
* Corresponding author. E-mail address: [email protected]
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function in some MRP II packages provides some assistance (see Harl 1983,
Nagendra et al. 1994), this is a very time consuming procedure. Another alternative is
the implementation of a shop floor control (SFC) system. But SFC systems are not
able to solve problems that have been created at the higher MRP planning level
(Bakke and Hellberg 1993, Taal and Wortmann 1997). Ram et al. (2006) try to deal
with unexpected shortages by using a flexible BOM instead of traditional methods
like safety stocks and safety lead times. Chen et al. provide a capacity requirements
planning system for twin Fabs of wafer fabrication. They adjust capacity to the actual
equipment loading but there is no capacity threshold.
Choi and Seo (2009) use capacity-filtering algorithms for flexible flow lines to
convert an infinite-capacity loading-profile to a finite-capacity loading-profile. This
rather theoretical approach needs some adjustments (additional constraints,
integration of dispatching rules, etc.) to deal with real-life problems. A finite-capacity
procedure for a Belgian steel company has been developed by Vanhoucke and Debels
(2009) in which a multi-objective function consisting of five different cost functions
is minimized under consideration of very company specific constraints.
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Netting
Lot sizing BOM Explosion
Offsetting
Gross requirements
Level 0
Gross requirements
Level i
i=i+1Net
requirements
i=0
Planned order
receipts
Planned order
releases
Scheduled receipts
Inventory
Complete Level i
Figure 1. Traditional Material Requirements Planning
It is desirable to prevent capacity problems at the MRP calculation stage using
an integrated approach of MRP and capacity planning. There are some research works
that address this problem. Billington and Thomas (1983, 1986) formulated linear
programming (LP) and mixed integer programming (MIP) models for capacity-
constrained MRP systems. Tardif (1995) developed an LP model for multiple
products with the same routeing (MRP-C).
Sum and Hill (1993) present a method that determines the release and due
dates of production orders while taking capacity constraints into account. Their
algorithm splits or combines production orders to minimize setup and inventory cost.
Taal and Wortmann (1997) focus on solving capacity problems using different
scheduling techniques like alternative routeing, splitting lot sizes, using safety stocks
and backward shift of late orders.
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Pandey et al. (2000) point out that complex algorithms are often not easily
understood by the planner and so they have developed a less mathematically
complicated system for finite capacity MRP (FCMRP), which is executed in two
stages. First, capacity-based production schedules are generated and then, in a second
step, the algorithm produces an appropriate material requirements plan to satisfy the
schedules obtained from the first stage. The model is restricted to lot for lot as the
only possible lot sizing rule and there is a single resource for each part type.
Wuttipornpun and Yenradee (2004) study a FCMRP system where they use a
variable lead time for MRP depending on the lot size, processing and setup time.
After scheduling jobs they reduce capacity problems by using alternative machines if
possible and adjusting the timing of jobs (starting the jobs earlier or delaying them).
Limitations of this model are: Bottleneck machines produce only one part, lot-for-lot
is the only lot sizing rule which is allowed and there is no overlap of production
batches. A further development of this approach is TOC-MRP (Wuttipornpun and
Yenradee 2007). With similar limitations the TOC philosophy is adopted in FCMRP
which results in a better performance compared to FCMRP.
Commercially available FCMRP software uses two different approaches for
including finite capacity: pre/post-MRP analysis and finite capacity scheduling
(Nagendra and Das 2001). Neither of them resolves the capacity problem during the
MRP run itself. Additionally computational effort increases substantially and so Lee
et al. (2009) proposed parallelising the MRP process and using a computational grid
which can exploit idle computer capacity.
Kanet and Stößlein (2010) describe ‘Capacitated ERP’ (CERP) – a variation
of MRP that takes resource capacity into account before exploding requirements to
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lower level components. The model is limited to one-stage production, single-level
BOM, single resource and no backorders.
The main approaches of MRP and capacity planning are summarized in Table
1. As you can see, considering finite capacity in Material Requirements Planning is an
old issue in production research but one which has not yet been solved satisfactorily.
Theoretical scheduling algorithms cause high calculating times for real word
problems and are not easy for planners to understand. MRP-CRP, MRP-SFC and
FCMRP approaches are also very time-consuming and attempt to solve the capacity
problem after an MRP run. Research contributions which try to integrate capacity
constraints into MRP are often limited to simple production environments.
Table 1. Main approaches of MRP and finite capacity planning
Approach References Limitations
Traditional MRP Orlicky (1975) fixed lead times, infinite capacity
MRP- CRP Harl (1983) identification of capacity problems after an MRP run, considerable participation of planner is
necessary
MRP-SFC Taal and
Wortmann (1997)
capacity problems are not solved on MRP level
FCMRP Pandey et al.
(2000)
capacity problems are not solved on MRP level,
lot sizing: only lot-for-lot, single resource for
each part type
Wuttipornpun and
Yenradee (2004)
capacity problems are not solved on MRP level,
lot sizing: only lot-for-lot, bottleneck machine:
one part type
Finite capacity
scheduling algorithms
Choi and Seo
(2009)
flexible flow line, theoretical approach,
constraints for real-life problems are missing
Vanhoucke and
Debels (2009)
company specific constraints
MRP and
integrated capacity
planning
Billington and
Thomas (1983)
mathematical programming formulation of the
problem, high computational effort for real-life
problems
Tardif (1995) same routeing for all products
Sum and Hill
(1993)
capacity-sensitive lot sizing with complex
algorithms (not easy for planners to understand,
high computational effort for real-life problems)
Taal and
Wortmann (1997)
fixed lead times
Kanet and
Stößlein (2010)
one-stage production, single-level BOM, single
resource, no backorders
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This paper aims to modify traditional MRP in two directions:
(1) by integrating capacity planning in the MRP run at each level in the BOM.
(2) by using variable lead times
For capacity adjustment, different measures like alternative routeings, safety stocks,
adjusting lot sizes and adding capacity are applied in a predefined sequence. Lead
times are not predefined fixed parameters. They are calculated dynamically,
dependent on lot sizes, inventory and required machine capacity. The presented
approach can handle multiple products, multiple resources, multi-stage production
and multi-level BOM. There is no restriction concerning the lot sizing rule. As in
traditional MRP all lot sizing rules can be used. An advantage of this approach in
practice is that it is based on the well-known MRP methodology. Dynamic lead times
and finite capacity are integrated at every stage of the MRP run to reduce the
shortcomings of MRP.
The paper is organized as follows. The integration of capacity planning is described in
Section 2, where each step is explained in detail. Section 3 illustrates the approach
with a numerical example. The conclusions are stated in Section 4.
2. Integrating capacity planning into the concept of MRP
In this section the basic ideas of integrating capacity requirements planning as well as
capacity adjustment into material requirements planning (MRP) are presented.
In the traditional MRP approach the items in the bill of material (BOM) are
sorted in levels according to the rule that items consist only of items from a higher
level, whereby end items (that are not part of any other items) are placed at level 0
(low level code). In Figure 2 the steps of Material and Capacity Requirements
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Planning (MCRP) are described. As in traditional MRP the MCRP starts with the
gross requirement of end items usually defined by the master production schedule.
The level index i is initialized with 0. For all items of level i netting and lot sizing
are performed. After completing level i the capacitating for all items and machines of
level i is executed. Furthermore, adjusted available capacity and capacity required
dynamic lead times for offsetting are determined in the capacitating step. This
dynamic lead time takes projected inventory, planned orders, scheduled receipts,
released open orders and machine loading into account. After completing the
capacitating for level i the offsetting is performed for all end items. The next step is
the BOM explosion as in traditional MRP. The gross requirements for the next level
1+i are defined by the planned order releases of levels with indices less than or equal
to i . Set 1= +i i and start the calculation for the next level. The procedure has
finished when all levels have been executed. After this overview all steps are
described in more detail.
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Netting
Lot sizing BOM Explosion
Offsetting
Gross requirements
Level 0
Gross requirements
Level i
i=i+1Net
requirements
i=0
Planned order
receipts
Planned order
releases
Scheduled receipts
Inventory
Complete Level i
Capacitating
Dynamic lead time
Complete Level i
Complete Level i
Available Capacity
Scheduled receipts
Figure 2. Material and Capacity Requirements Planning (MCRP)
2.1. Netting
In the netting step, the net requirements are determined by taking into account the
gross requirements, scheduled receipts and inventory. The gross requirements for the
end items are predefined by the master production schedule. The gross requirements
for sub items are set by the bill of material explosion during MCRP. Scheduled
receipts are converted to planned order receipts and may be released or not released to
production. Sub items needed for scheduled receipts are allocated in stock or taken
from stock. Netting is performed as in traditional MRP. Net requirements are
calculated under consideration of projected inventory, safety stock and gross
requirements. A more sophisticated approach can take dynamic planned safety stocks
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into account as Kanet et al. (2010) suggest in their work. Netting is supported by
Table 2.
Table 2. MCRP table for one item
Period 1 2 3 4 5 6 7 8 9 …
Gross requirements from MPS or see BOM explosion
Scheduled receipts see convert an order
Projected inventory see netting
Net requirement see netting
Planned order receipts see lot sizing
Calculated lead time ( ),j kl see capacity planning
Planned order releases see offsetting
2.2. Lot sizing
To trade off changeover cost against holding cost a lot sizing rule is applied. In this
approach all known lot sizing methods for MRP can be applied. If there are no
essential changeover costs or if enough excess capacity is available the Lot for Lot
strategy is recommended to reduce inventory (see Haddock and Hubicky 1989). In all
other cases dynamic rules, for instance Groff (see Groff 1979) or Fixed Order Period
(see Hopp and Spearman 2008) should be applied. The results of the lot sizing are the
due dates for the planned orders and the batch size of the orders (the two are called
planned order receipts). A planned order receipt of 10 items in period 5 means, that it
is planned to finish 10 items by the end of period 5. Lot sizing is also supported by
Table 2.
2.3. Capacity planning
This step is compared to MRP new and is applied for all items manufactured in-
house. Purchased parts, for which subcontracting in the sense of capacity buying is
performed, can be treated as parts manufactured in-house, whereby information of the
available capacity from the supplier is necessary. All other purchased items are
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treated with predefined planned lead times as in traditional MRP (and no capacity
planning is performed). The capacity planning consists of two main steps: capacity
adjustment and calculation of the dynamic lead time and the release dates.
2.3.1. Capacity adjustment
The available capacity is based on shift models, working time and number of workers
and may be adjusted. Scheduled receipts are determined by the number of items and a
due date. The required capacity for scheduled receipts can be calculated under
consideration of lot sizes, processing times and set up times and will be referred to as
scheduled capacity receipts. In analogy the required capacities of planned order
receipts are referred to as planned capacity receipts. The cumulated values are
calculated by the sum over the time periods. The cumulated required capacity is
defined as the sum of the cumulated scheduled capacity receipts and the cumulated
planned capacity receipts. The free cumulated capacity is the difference between the
cumulated available capacity and the cumulated required capacity and must be non-
negative to ensure capacity feasibility. The calculation is supported by Table 3, the
explanation of the capacity envelope follows in the chapter 2.3.2.
Table 3. MCRP table for one capacity group
Period 1 2 3 4 5 6 7 8 9 …
Available capacity
Scheduled capacity receipts ( )capSR
Planned capacity receipts ( )capPO
Cumulated available capacity ( )ia
Cumulated required capacity ( )ir
Free cumulated capacity ( )−i ia r
Capacity envelope ( )ie
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If the planned capacity receipts are higher than the net available capacity this is not
necessarily a reason for a capacity infeasible schedule because the scheduled capacity
receipts as well as the planned capacity receipts allocate the whole required capacity
to the due date (but it may be produced in earlier periods). To achieve capacity
feasibility, the cumulated available capacity must be high enough to cover the
cumulated required capacity.
If the cumulated required capacity is higher than the cumulated available
capacity, there is a capacity problem and no capacity feasible production schedule can
be found (see Hübl et al. 2009). The following countermeasures can be considered:
(1) Alternative routeings
(2) Relaxing safety stocks
(3) Applying lot splitting with consecutive processing
(4) Applying lot summarization
(5) Adjusting available capacity by adding capacity (over time, more staff, etc.)
(6) Accepting tardiness respectively by backlog or postponing gross requirement
in the master plan
The first measure for decreasing required capacity is choosing alternative routings
(see Taal and Wortmann 1997). Production orders, planned on the bottleneck resource
in overloaded periods, should be planned on alternative resources if it is possible to
unload the bottleneck resource. If the capacity of alternative resources is short, lot
splitting with simultaneous processing using alternative resources is suggested.
Measures (2), (3) and (4) require starting the netting and lot sizing with
changed parameters on the current level. For the further discussion let T be the latest
period at which a capacity problem is given (i. e. cumulated required capacity is
higher than the cumulated available capacity).
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Relaxing safety stock is a measure which is also proposed by Taal and
Wortmann (1997) but with a lower priority than is used in this approach. It can easily
be performed by running the netting and lot sizing with safety stocks equal to zero as
long as the net requirements have an influence on the capacity problem. More
accurately, all net requirements which are combined to planned order receipts with
due dates before or equal to T should be calculated assuming safety stock to be zero.
All others should be calculated with the predefined safety stock. This postponement
can solve or improve the capacity problem, reduce the inventory and increase the
danger of stock outs because of unforeseen events (machine breakdown, scrap,
rework, demand fluctuation, etc.).
Lot splitting with consecutive processing is very useful if only short or no set
up time is required and net requirements of more than one period are combined to one
batch. To execute lot splitting, lot sizing is based on an adjusted rule for all batches
which combine net requirements with due dates before T and with due dates after T.
All these batches are divided into two lots. The first lot combines all net requirements
with due dates earlier than or equal to T and the second the remaining net
requirements. The second batch should be planned as late as possible to reduce
inventory. Lot splitting can solve or improve the capacity problem, reduce inventory
and increase change over costs.
Lot summarization can be useful if there is an essential change over time and
the same item is planned in different orders, all with due dates before T. In this case
all planned orders with due dates before or equal to T are combined to one new
planned order receipt. Lot summarization can solve or improve the capacity problem,
increase inventory and reduce changeover costs.
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If the first four mentioned measures do not solve the capacity problem,
additional capacity (e.g. over time, more staff, additional shift, etc.) is needed within
the allowed and possible capacity boundaries. In general, this measure should solve
the capacity problem or the capacity problem has to be accepted, resulting in backlog.
Of course additional costs are thereby incurred.
If all measures do not solve the capacity problem, tardiness of at least one job
has to be accepted. In order to ensure a consistent procedure a reduction or a
postponement of gross requirements in the master plan is recommended whereby it is
necessary to start the whole procedure again at level zero. One way to find suitable
master plan orders (for reduction or postponement) is to apply pegging (see Hopp and
Spearman 2008). The following steps have to be performed: Step 1: Searching the due
date T1 of master plan orders which lies the furthermost in the future and is connected
with a planned order at the current level whose due date is earlier than or equal to T.
Step 2: Select master plan orders with due dates before T1 which are not important
(e.g. a stock order, customer acceptance of later delivery date, bad contribution
margin and no strategically unimportant order from a C customer, etc.) and in which
required capacity at the current level is greater than the missed capacity, and postpone
them until after T1 or delete them.
For the capacity adjustment a specific product sequence is defined. Depending
on the importance of different managerial goals, one of the following proposed
criteria can be chosen to build up the sequence.
• importance of service level (starting with the item with the least important
service level)
• holding cost (starting with the item with the highest holding cost per unit)
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For measures (2) and (3) the sequence should be applied as defined above. For
measure (4) the sequence of the service level and the holding cost criteria should be
applied in the reversed order.
The described measures for capacity adjustment are applied in the order in
which they are listed above and for the products in the predefined sequence. If the
capacity problem is solved, then the capacity adjustment procedure has to be stopped.
If the measures applied to the current level do not lead to capacity feasibility, the
measures can be applied to lower levels. After applying these measures, we assume
that the cumulated required capacity is less than the cumulated available capacity.
Furthermore, if possible (e.g. at the end of the planning horizon) the available
capacity should be reduced.
2.3.2. Calculation of dynamic lead times and release dates
Now the second step in capacity planning is performed. This is the calculation of the
dynamic lead times and the release dates. The lead time calculation is based on a
predefined product sequence, starting with the item which should be produced as late
as possible. This can be a different sequence to the one used for capacity adjustment.
In order to build up the sequence one of the following criteria can be used:
• holding cost (starting with the item with the highest holding cost per unit)
This criterion reduces inventory holding costs.
• set up (starting with the item which should be produced last)
This criterion reduces changeover costs if set up times depend on the
sequence.
• tardiness (starting with the item with the lowest tardiness penalty cost)
This criterion reduces tardiness for items with the highest penalty costs.
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The predefined sequence should be consistent over all levels supporting a first-in-
first-out principle along the routeing.
To prepare the dynamic lead time calculation the capacity envelope is
determined (see also Table 3). The capacity envelope is the cumulated capacity usage
based on the cumulated required capacity. The envelope is piecewise parallel (vertical
translation) to the cumulated available capacity or parallel to the time axis and is the
lowest possible envelope above the cumulated required capacity. In Figure 3 the
capacity envelope is illustrated as an example.
Scheduled receipts or
planned orders of levels with lower level codes
Planned order Cumulated available
capacity
Cumulated required
capacity
Capacity envelope
Capacity
Time
1 2 3
a1-r1
a2-r2
a3-r3
e2
e3
e1
Figure 3. Capacity envelope determination
To get the value ie of the capacity envelope at period i it is necessary to
determine the minimal distance 1 1min( , ,..., )+ +− − −i i i i N Na r a r a r from cumulated
available capacity to cumulated required capacity in the periods i, i+1, ... n.
Subtracting this minimal distance from the cumulated available capacity in period i
yields the capacity envelope at period i. Between the times i-1 and i the capacity
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envelope is a piecewise linear function which is constant and equal to the value of the
capacity envelope in period i-1 or a linear function of which the slope is the difference
1−−i ia a between the cumulated available capacity values in period i and period i-1.
The major value of these two functions determines the value of the capacity envelope.
In the following formula the calculation of the envelope is defined.
( )( )( ) ] ]1 1
1 1
min( , ,..., )
( ) max , , for 1,
discrete time capacity envelope in period i
( ) continuous time capacity envelope with respect to time t
cumulated requi
i i i i i i N N
i i i i
i
i
e a a r a r a r
e t e e a a t i t i i
e
e t
r
+ +
− −
= − − − −
= + − − ∈ −
L
L
L red capacity in period i
cumulated available capacity in period i
number of periods in the planning horizon
ia
N
L
L
(1)
The idea of release date determination is explained in Figure 4. The cumulated
required capacity jr is reduced by the scheduled receipts and planned orders of levels
with lower level codes ( jcapSR ) and by the first k-ranked planned orders of the
current level based on the criteria explained above (1=
∑k
ji
i
capPO ). This capacity value
,j kc for the k-ranked planned order in period j is described by the following formula:
,
1
,
, for j , 1,...1 and 1,...
cumulated required capacity to period j-1
plus all orders with due date j and not one of the first k-ranked
capacity for the schedu
=
= − − = − =∑
L
L
k
j k j j ji j
i
j k
j
c r capSR capPO N N k K
c
capSR led receipts in period j and
planned orders of levels with lower level code
capacity for the planned order with due date j and i-ranked
required cumulated capacity to period j
number of per
L
L
L
ji
j
capPO
r
N iods in the planning horizon
number of planned orders with due date jLjK
(2)
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Now the capacity value ,j kc is intersected with the capacity envelope ( )e t for
determining the lead time ,j kl and the release date ,j kt for the k-ranked planned order.
The next formula provides detailed information for calculating these two values.
,
,
1
, ,
,
,
,
calculated lead time of the k-ranked planned order with due date j
release date to the k-ranked planned order with due date j
cumulated required capacity to
j j k
j k
j j
j k j k
j k
j k
j k
e cl
a a
t j l
l
t
c
−
−=
−
= −
L
L
L period j-1
plus all orders with due date j and not one of the first k-ranked
cumulated available capacity to period j
capacity envelope in period j
j
j
a
e
L
L
(3)
Scheduled receipts or
planned orders of levels with lower level codes
Planned order
Cumulated required capacity
Capacity envelope
Capacity
Time1 2 3
c3,1
capSR3
capPO31
capPO32
capPO33
l3,1
t3,1
e3-c3,1
Release dates
e3
Figure 4. Release date determination
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The determination of the lead time and the release date for the first-ranked order in
period 3 is visualized in Figure 4. For the release date calculation in the whole
planning horizon it is necessary to start at the furthermost future time period within
the planning horizon. If the release date of the first-ranked planned order of the last
period in the planning is determined, the capacity value is reduced by the next
planned order. This value is intersected with the capacity envelope and so on. If this
procedure is completed on the last due date, then the next earlier due date is chosen.
The scheduled capacity receipts are subtracted first and then the calculation of the
release date is performed with the predefined sequence again until all planned orders
are finished. The calculated lead time should be entered in Table 2. The release date
for the k-ranked planned order is the latest possible time when the available capacity
between the release date and the due date covers the capacity needed to produce the
first k-ranked planned orders as well as the scheduled receipts.
2.3.3. Building machine groups
The combination of several machines into one machine group is useful but
requires some adjustment of the calculation procedure for the dynamic lead time. If n
equivalent machines are combined into one group, the group available capacity is of
course the available capacity of the individual machine multiplied by n. But if an
order is produced only on one machine and is not split among several machines
simultaneously, the order processing time is not equal to required capacity over
available group capacity. We have to take into account the number of machines
combined into one machine group. Hence the correct calculation of the order
processing time is: order processing time is equal to required capacity multiplied by n
over available group capacity. Consequently, to determine the dynamic lead time for a
machine group the following steps should be performed:
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(1) Group the scheduled receipts and the planned orders in n order groups (n is the
number of equivalent machines)
(2) Calculate the release dates for each order group according to the above
formula using required capacity multiplied by n instead of required capacity.
To find the order groups, the predefined order sequence (the same as for the
lead time calculation) should be taken into account. Furthermore, the required
capacity for each group should be approximately the same. The first n orders should
be taken (starting with the scheduled receipts and then the ranked planned orders) and
allocated to the n groups. The order groups should be arranged by ascending rank in
required capacity. The next n orders should be taken, arranged by descending rank
and allocated to the group. This should be applied to the next n orders and so on until
all orders have been allocated.
2.4. Offsetting
In traditional MRP the release date is equal to the due date minus the predefined lead
time or, in more advanced systems, equal to a fixed lead time part and the dynamic
lead time part taking into account the lot size and processing time. In the MCRP
approach the offsetting is based on the dynamic determination of the release date
according to Equation (3). Consequently, the planned order release is determined by
rounding down the calculated release date. In Table 2 the row “planned order
releases” supports this calculation. A planned order release of 10 items in period 5
means that the release of a production order of 10 items is planned just before the
beginning of period 5 (at the end of period 4).
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2.5. BOM Explosion
Based on planned order receipts the gross requirements for the next level are
calculated by the bill of material explosion. This is done as in traditional MRP. The
release date of the planned order receipt (of the lower level item) is equal to the due
date of the gross requirements (of the higher level item). In Table 2 all item-related
calculations are supported.
2.6. Predefined parameters for the MCRP
To summarize the MCRP approach the predefined parameters for customizing the
system are listed in the following table. For a better comparison with MRP the
parameters for each step are specified for both procedures.
Table 4. Predefined parameters for MCRP and MRP
Step MCRP MRP
Netting safety stock safety stock
Lot Sizing lot sizing rule lot sizing rule
Capacity Planning allowed countermeasures for capacity
problems, allowed available capacity
levels, capacity boundary, product
sequence for capacity adjustment, product
sequence for lead time calculation,
processing times, setup times, machine
item allocation
lacks in traditional
MRP
Offsetting no predefined parameters (dynamic lead time
is calculated) planned lead time
BOM Explosion BOM BOM
2.7. Converting a planned order into a production order
After the MCRP run, planned orders have to be converted into scheduled receipts,
sometimes called production orders for in house manufactured items and purchase
orders for purchased items. This conversion causes scheduled receipts in the next
MCRP run and a reservation of the sub items needed, leading to a reduction of the
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available on hand inventory of the sub items. As in traditional MRP, the conversion
should be done at the latest possible time to ensure customer demand oriented
production or purchasing orders. Taking this rule into account, the release date of a
scheduled receipt is in the past or in period 1.
2.8. Releasing an order
A converted planned order (scheduled receipt) has to be released to production
(released scheduled receipt) meaning that the production staff are allowed to start the
production process. This release causes a removal of the sub items from the stock and
a cancelation of the reservation made at the time of conversion. Similar to traditional
MRP the release should be done at the latest possible time and after ensuring the
availability of all sub items, tools and resources needed.
For MCRP we suggest that conversion and release should be performed
simultaneously at the latest possible time (just before the release date) and after
ensuring the availability of all sub items, tools and resources needed.
2.9. Dispatching
After release production can be started. In general there are several released
production orders waiting for processing. To prioritize production orders the earliest
due date rule is recommended to minimize total tardiness (see Baker 1984), whereby
the due date refers to the due date of the corresponding planned order (Modified Due
Date MDD). If there is more than one order with the same due date the reverse
predefined product sequence (for the lead time calculation) is used additionally. By
applying this rule a good adherence to the plan should be achieved.
It is important to note that the task of capacity planning in MCRP is not
detailed scheduling in the sense of calculating exact start and completion times. The
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objective is to support material requirements planning by ensuring capacity feasible
plans (because of the fact that cumulated available capacity is higher than cumulated
required capacity) and lowest possible inventory (because of shortest capacity feasible
lead times).
As a result of the planning procedure it may be possible that a production
order lies within another production order (release date A ≤ release date B ≤ due
date B ≤ due date A) with the same item produced. In this case the summarization of
the two orders is recommended.
2.10. Completing the order
After finishing an order the items should be booked to the inventory in real time and
the released scheduled receipt has to be deleted in real time. For orders which take a
long time it is useful to partly book the items to inventory and to simultaneously
reduce the scheduled receipts in order to ensure a realistic cumulated required
capacity. Backlog and orders which are late are added to the scheduled receipts in
period one.
3. Illustration of the concept
The following example is provided to show how the MCRP approach may be used. In
this example two end items A and B are considered. Item A consists of one item X
and one item Y. Item B is assembled from one item Y and one item Z. Table 5
delivers necessary input data for all items. The available capacity per period of the
two machines M0 and M1 is 420 TU. The predefined product sequence for capacity
adjustment and lead time calculation is A, B (for M0) and X, Y, Z (for M1).
Table 5. Input data for all items
Item A B X Y Z
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Safety stock 10 10 10 10 10
Lot sizing FOP 3 FOP 3 FOP 3 FOP 3 FOP 3
Processing time 14 9 7 5 8
Setup time 45 40 30 35 20
Allocated machine M0 M0 M1 M1 M1
On hand inventory 19 65 50 50 59
In the planning horizon of 10 periods the gross requirements of the MPS and the
scheduled receipts are listed in Table 6. With this information projected inventory and
net requirements can be computed as in traditional MRP under consideration of the
safety stock. For determination of planned order receipts the lot sizing rule fixed order
period (FOP 3) is applied.
Table 6. MCRP table for A and B
Item A
Period 1 2 3 4 5 6 7 8 9 10
Gross requirements 10 10 10 20
30 10 10 10 10
Scheduled receipts 20
Projected inventory 19 29 19 9
Net requirements 0 0 1 20 0 30 10 10 10 10
Planned order receipts 0 0 21 0 0 50 0 0 20 0
Item B
Period 1 2 3 4 5 6 7 8 9 10
Gross requirements 20 20 20 40 20 20 20 20 20 20
Scheduled receipts
Projected inventory 65 45 25 5
Net requirements 0 0 5 40 20 20 20 20 20 20
Planned order receipts 0 0 65 0 0 60 0 0 40 0
By using the MCRP table for machines cumulated available capacity and cumulated
required capacity are determined. The difference cumulated available capacity minus
cumulated required capacity is equal to the free cumulated capacity. A negative sign
indicates a capacity problem in periods 3 and 6. For capacity adjustment the
countermeasures “relax safety stock” and “lot splitting” are applied in detail.
Table 7. MCRP table for M0
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Machine M0
Period 1 2 3 4 5 6 7 8 9 10
Available capacity 420 420 420 420 420 420 420 420 420 420
Scheduled capacity receipts 325
Planned capacity receipts
964
1325
725
Cumulated available capacity 420 840 1260 1680 2100 2520 2940 3360 3780 4200
Cumulated required capacity 325 325 1289 1289 1289 2614 2614 2614 3339 3339
Free cumulated capacity 95 515 -29 391 811 -94 326 746 441 861
Capacity envelope
3.1.1. Capacity adjustment by relaxing safety stock
We start relaxing safety stock with item A according to the predefined sequence. The
latest period at which the capacity period is at hand is T = 6. As the planned order of
item A in period 6 summarizes net requirements until period 8, safety stock should be
relaxed until period 8. The calculation of the planned order receipts with relaxed
safety stock can be found in Table 8. Relaxing safety stock only for item A does not
lead to a capacity feasible production plan, so the same procedure is followed for item
B, where safety stock should also be relaxed until period 8. Table 9 shows that now
the cumulated required capacity is always less than cumulated available capacity and
the capacity envelope can be computed according to Equation (1). Now for the end
items A and B the determination of dynamic lead times with Equation (3) can be
carried out to get planned order releases. For example the lead time calculation for the
planned order receipts of item A in period j = 4 is shown in Equation (4) . The values
of the required cumulated capacity, the cumulated available capacity and the capacity
envelope are taken from Table 9. There are no scheduled receipts of item A in period
4 and only one planned order of 41 pieces. The capacity of this planned order is
received under consideration of the processing and setup time of item A (see Table 5).
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( )4,1 4 41
4 4,1
4,1
4 3
1659 14 41 45 1040
1674 10101.5095
1680 1260
= − = − × + =
− −= = =
− −
c r capPO
e cl
a a
(4)
Table 8. MCRP table for A and B with relaxed safety stock
Item A
Period 1 2 3 4 5 6 7 8 9 10
Gross requirements 10 10 10 20 0 30 10 10 10 10
Scheduled receipts 20
Projected inventory 19 29 19 9 -11
Net requirements 0 0 0 11 0 30 10 10 20 10
Planned order receipts 0 0 0 41 0 0 40 0 0 10
Calculated lead time 0 0 0 1.5 0,0 0,0 1.4 0,0 0,0 0.4
Planned order releases 0 0 41 0 0 40 0 0 0 10
Item B
Period 1 2 3 4 5 6 7 8 9 10
Gross requirements 20 20 20 40 20 20 20 20 20 20
Scheduled receipts
Projected inventory 65 45 25 5 -35
Net requirements 0 0 0 35 20 20 20 20 30 20
Planned order receipts 0 0 0 75 0 0 70 0 0 20
Calculated lead time 0 0 0 1.7 0,0 0,0 1.6 0,0 0,0 0.5
Planned order releases 0 0 75 0 0 70 0 0 0 20
Table 9. MCRP table for M0 with relaxed safety stock
Machine M0
Period 1 2 3 4 5 6 7 8 9 10
Available capacity 420 420 420 420 420 420 420 420 420 420
Scheduled capacity receipts 325
Planned capacity receipts 1334 1275 405
Cumulated available capacity 420 840 1260 1680 2100 2520 2940 3360 3780 4200
Cumulated required capacity 325 325 325 1659 1659 1659 2934 2934 2934 3339
Free cumulated capacity 95 515 935 21 441 861 6 426 846 861
Capacity envelope 414 834 1254 1674 2094 2514 2934 2934 2934 3339
The calculated dynamic lead times and explosion of the bill of material define the
gross requirements for the sub items and planned order receipts for X, Y and Z are
calculated in Table 10 in the same way as was performed for A and B.
Table 10. MCRP table for X, Y, Z
Item X
Period 1 2 3 4 5 6 7 8 9 10
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Gross requirements 41 40 10
Scheduled receipts
Projected inventory 50 50 9
Net requirements 0 1 0 0 40 0 0 0 10 0
Planned order receipts 0 1 0 0 40 0 0 10 0 0
Item Y
Period 1 2 3 4 5 6 7 8 9 10
Gross requirements 116 110 30
Scheduled receipts
Projected inventory 50 50 -66
Net requirements 0 76 0 0 110 0 0 0 30 0
Planned order receipts 0 76 0 0 110 0 0 30 0 0
Item Z
Period 1 2 3 4 5 6 7 8 9 10
Gross requirements 75 70 20
Scheduled receipts
Projected inventory 59 59 -16
Net requirements 0 26 0 0 70 0 0 0 20 0
Planned order receipts 0 26 0 0 70 0 0 20 0 0
Comparing cumulated available and required capacity for M1 in Table 11 indicates a
capacity infeasibility in period 5, which can be removed by relaxing safety stock of
item X until period 7 (see Table 12 and Table 13). All in all relaxing safety stock of
the items A, B and X delivers a capacity feasible production plan.
Table 11. MCRP table for M1
Machine M1
Period 1 2 3 4 5 6 7 8 9 10
Available capacity 420 420 420 420 420 420 420 420 420 420
Scheduled capacity receipts
Planned capacity receipts 680 1475 465
Cumulated available capacity 420 840 1260 1680 2100 2520 2940 3360 3780 4200
Cumulated required capacity 0 680 680 680 2155 2155 2155 2620 2620 2620
Free cumulated capacity 420 160 580 1000 -55 365 785 740 1160 1580
Capacity envelope
Table 12. MCRP table for X with relaxed safety stock
Item X
Period 1 2 3 4 5 6 7 8 9 10
Gross requirements 41 40 10
Scheduled receipts
Projected inventory 50 50 9 9 9 -31
Net requirements 0 0 0 0 31 0 0 10 10 0
Planned order receipts 0 0 0 0 31 0 0 20 0 0
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Calculated lead time 0 0 0 0 0,6 0,0 0,0 0,4 0,0 0,0
Planned order releases 0 0 0 0 31 0 0 20 0 0
Table 13. MCRP table for M1 with relaxed safety stock
Machine M1
Period 1 2 3 4 5 6 7 8 9 10
Available capacity 420 420 420 420 420 420 420 420 420 420
Scheduled capacity receipts
Planned capacity receipts 643 1412 535
Cumulated available capacity 420 840 1260 1680 2100 2520 2940 3360 3780 4200
Cumulated required capacity 0 643 643 643 2055 2055 2055 2590 2590 2590
Free cumulated capacity 420 197 617 1037 45 465 885 770 1190 1610
Capacity envelope 375 795 1215 1635 2055 2055 2170 2590 2590 2590
3.1.2. Capacity adjustment by lot splitting
In order to resolve the capacity problem pointed out in Table 7, countermeasure lot
splitting can also be successful. Starting again with item A (compare predefined
sequence) the lot in period 6 is split into two lots: one is planned in period T = 6 (lot
size 30) and the other one is planned after T (lot size 20 in period 7). The MCRP table
for M0 shows that after application of this measure a capacity problem still remains
in period T = 3. So for item B the lot in period 3 (lot size 65) is split into two lots: one
in period 3 (lot size 5) and one in period 4 (lot size 60). All details can be found in
Table 14. Filling out the MCRP table for M0 again (see Table 15) shows that the
capacity problem was solved and the MCRP run can be executed for the next level.
Table 14. MCRP table for A with lot splitting
Item A
Period 1 2 3 4 5 6 7 8 9 10
Gross requirements 10 10 10 20 0 30 10 10 10 10
Scheduled receipts 20
Projected inventory 19 29 19 9
Net requirements 0 0 1 20 0 30 10 10 10 10
Planned order receipts 0 0 21 0 0 30 20 0 20 0
Calculated lead time 0 0 1.7 0,0 0,0 1.1 0.8 0,0 0.8 0,0
Planned order releases 0 21 0 0 30 0 20 0 20 0
Item B
Period 1 2 3 4 5 6 7 8 9 10
Gross requirements 20 20 20 40 20 20 20 20 20 20
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Scheduled receipts 0 0 0 0 0 0 0 0 0 0
Projected inventory 65 45 25 5
Net requirements 0 0 5 40 20 20 20 20 20 20
Planned order receipts 0 0 5 60 0 60 0 0 40 0
Calculated lead time 0 0 1.1 1.9 0,0 1.4 0,0 0,0 1.0 0,0
Planned order releases 0 5 60 0 60 0 0 0 40 0
Table 15. MCRP table for M0 with lot splitting
Machine M0
Period 1 2 3 4 5 6 7 8 9 10
Available capacity 420 420 420 420 420 420 420 420 420 420
Scheduled capacity receipts 325 0 0 0 0 0 0 0 0 0
Planned capacity receipts 0 0 424 580 0 1045 325 0 725 0
Cumulated available capacity 420 840 1260 1680 2100 2520 2940 3360 3780 4200
Cumulated required capacity 325 325 749 1329 1329 2374 2699 2699 3424 3424
Free cumulated capacity 95 515 511 351 771 146 241 661 356 776
Capacity envelope 325 694 1114 1534 1954 2374 2699 3004 3424 3424
Table 16 and Table 17 show the MCRP tables for the sub items X, Y, Z and machine
M1. In the periods 2 and 3 there is still a capacity infeasibility, which can be removed
by applying lot splitting again. There is no planned order receipt of X in the first three
periods so lot splitting is applied for item Y first. The lot in period 2 (lot size 136) is
divided into two lots: one in period 2 with lot size 46 and the second lot in period 4
(no net requirements in period 3) with lot size 90. However this measure does not
supply enough capacity reduction in period 2 and so for sub item Z the lot in period 2
is split too: one lot in period 2 (lot size 16) and one lot in period 4 (lot size 60). Table
18 shows that lot splitting of a total of four lots was successful and the result is a
capacity feasible production plan.
Table 16. MCRP table for X, Y and Z
Item X
Period 1 2 3 4 5 6 7 8 9 10
Gross requirements 21
30
20
20
Scheduled receipts
Projected inventory 50 29 29 29 -1
Net requirements 0 0 0 11 0 20 0 20 0 0
Planned order receipts 0 0 0 31 0 0 20 0 0 0
Item Y
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Period 1 2 3 4 5 6 7 8 9 10
Gross requirements 86 90 20 40 20
Scheduled receipts
Projected inventory 50 -36
Net requirements 46 0 0 90 0 20 40 20 0 0
Planned order receipts 46 0 0 110 0 0 60 0 0 0
Item Z
Period 1 2 3 4 5 6 7 8 9 10
Gross requirements 65 60 40
Scheduled receipts
Projected inventory 59 -6
Net requirements 16 0 0 60 0 0 40 0 0 0
Planned order receipts 16 0 0 60 0 0 40 0 0 0
Table 17. MCRP table for M1
Machine M1
Period 1 2 3 4 5 6 7 8 9 10
Available capacity 420 420 420 420 420 420 420 420 420 420
Scheduled capacity receipts 0 0 0 0 0 0 0 0 0 0
Planned capacity receipts 0 1343 0 247 135 340 170 335 0 0
Cumulated available capacity 420 840 1260 1680 2100 2520 2940 3360 3780 4200
Cumulated required capacity 0 1343 1343 1590 1725 2065 2235 2570 2570 2570
Free cumulated capacity 420 -503 -83 90 375 455 705 790 1210 1630
Capacity envelope
Table 18. MCRP table for M1 with lot splitting
Machine M1
Period 1 2 3 4 5 6 7 8 9 10
Available Capacity 420 420 420 420 420 420 420 420 420 420
Scheduled capacity receipts 0 0 0 0 0 0 0 0 0 0
Planned capacity receipts 0 413 0 1232 135 340 170 335 0 0
Cumulated available capacity 420 840 1260 1680 2100 2520 2940 3360 3780 4200
Cumulated required capacity 413 413 1645 1780 2120 2290 2625 2625 2625
Free cumulated capacity 420 427 847 35 320 400 650 735 1155 1575
Capacity envelope 385 805 1225 1645 1780 2120 2290 2625 2625 2625
4. Conclusion
In this paper an approach for coping with the finite capacity of machines in an MRP
procedure was developed (MCRP). An additional procedure, capacitating, was
inserted between the steps lot-sizing and offsetting to guarantee capacity feasible
production plans. To reach this result different measures for capacity adjustment have
been proposed and two of them (relaxing safety stock and lot splitting) have been
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successfully applied in a detailed example. Additionally, lead times for offsetting are
calculated dynamically to take lot sizes, inventory and the required machine capacity
into account.
Some limitations of the proposed approach are the lack of stochastic influences and
the lack of a safety lead time which could be advantageous mainly to cope with
unreliability in supply (see van Kampen et al. 2010). A safety lead time can be
integrated easily by adding this time into the calculation of the dynamic lead time.
Furthermore there is no guarantee that the listed countermeasures lead to a capacity
feasible production plan. If the application of all countermeasures is not successful,
the master production schedule (MPS) has to be changed or otherwise tardiness of
some jobs has to be accepted.
On the other hand some managerial goals (e.g. increasing service level, reducing
holding costs, changeover costs or tardiness) can be influenced positively by choosing
adequate parameters. Integrating capacity planning in an MRP run can supersede or at
least reduce a time consuming revision of the schedules by the user.
In real world implementation most firms integrate traditional MRP in their ERP.
Because of the weaknesses of MRP (no capacity planning and fixed lead times) the
planners have to adapt the plans subsequently to ensure feasibility – this job list
adaption is in general a difficult and time consuming task. The suggested approach
has advantage over traditional MRP as well as MRP-CRP (Harl, 1983), MRP-SFC
(Taal and Wortmann, 1997) and FCMRP (Pandey et al., 2000). The capacity
planning is performed during the MRP-Run between lot sizing and offsetting, a load
depending lead time is calculated and therefore in more cases than in traditional MRP
capacity feasible planes are determined. Another further available development of
MRP is finite capacity scheduling algorithm (for instance Billington and Thomas,
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1983; Sum and Hill, 1993; Cho and Seo, 2009) offered in Advanced Planning
Systems like Detailed Scheduling in SAP/APO. General scheduling algorithms are
not often used in industrial environments because of lack of understanding, missing
constraints for real-life problems, deviation of the deterministic model for the
stochastic real world and the long calculation times needed.
For further research material capacity requirement planning with dynamic lead
times should be implemented in simulation software to test more complex scenarios
and to compare the performance of MCRP with traditional MRP.
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References
Baker, K., 1984. Sequencing rules and due-date assignments in a job shop.
Management Science, 30(9), 1093-1104.
Bakke, N. A. and Hellberg, R., 1993. The challenges of capacity planning.
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Netting
Lot sizing BOM Explosion
Offsetting
Gross requirements Level 0
Gross requirements Level i
i=i+1 Net requirements
i=0
Planned order receipts
Planned order releases
Scheduled receipts Inventory
Complete Level i
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Netting
Lot sizing BOM Explosion
Offsetting
Gross requirements Level 0
Gross requirements Level i
i=i+1 Net requirements
i=0
Planned order receipts
Planned order releases
Scheduled receipts Inventory
Complete Level i
Capacitating
Dynamic lead time
Complete Level i
Complete Level i
Available Capacity Scheduled receipts
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Scheduled receipts or planned oders of levels with lower level codes
Planned order
Cumulated available capacity
Cumulated required capacity
Capacity envelope
e3
a3-r3
e2
e1
a1-r1
a2-r2
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Scheduled receipts or planned oders of levels with lower level codes
Planned order
Cumulated required capacity
Capacity envelope
Release dates
e3 e3-c3,1
l3,1
capSR3
capSR3
capSR3
capSR3
l3,1
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